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Chapter 4 Section 2 The Quantum Model of the Atom Electrons as Waves • French scientist Louis de Broglie suggested that electrons be considered waves confined to the space around an atomic nucleus. • It followed that the electron waves could exist only at specific frequencies. • According to the relationship E = hν, these frequencies corresponded to specific energies—the quantized energies of Bohr’s orbits. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Electrons as Waves, continued • Electrons, like light waves, can be bent, or diffracted. • Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening. • Electron beams, like waves, can interfere with each other. • Interference occurs when waves overlap. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom The Heisenberg Uncertainty Principle • German physicist Werner Heisenberg proposed that any attempt to locate a specific electron with a photon knocks the electron off its course. • The Heisenberg uncertainty principle states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom The Schrödinger Wave Equation • In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves. • Together with the Heisenberg uncertainty principle, the Schrödinger wave equation laid the foundation for modern quantum theory. • Quantum theory describes mathematically the wave properties of electrons and other very small particles. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom The Schrödinger Wave Equation, continued • Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated. • Instead, they exist in certain regions called orbitals. • An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Electron Cloud Click below to watch the Visual Concept. Visual Concept © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Atomic Orbitals and Quantum Numbers • Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. • The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron. • The angular momentum quantum number, symbolized by l, indicates the shape of the orbital. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Atomic Orbitals and Quantum Numbers, continued • The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus. • The spin quantum number has only two possible values—(+1/2 , −1/2)—which indicate the two fundamental spin states of an electron in an orbital. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Quantum Numbers and Orbitals Click below to watch the Visual Concept. Visual Concept © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Shapes of s, p, and d Orbitals © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Electrons Accommodated in Energy Levels and Sublevels © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Electrons Accommodated in Energy Levels and Sublevels © Houghton Mifflin Harcourt Publishing Company Chapter 4 Section 2 The Quantum Model of the Atom Quantum Numbers of the First 30 Atomic Orbitals © Houghton Mifflin Harcourt Publishing Company